High sensitivity and amenability to miniaturization for field-portable applications have helped to make ion mobility spectrometry (IMS) an important technique for the detection of many compounds, including narcotics, explosives, and chemical warfare agents as described, for example, by G. Eiceman and Z. Karpas in their book entitled “Ion Mobility Spectrometry” (CRC, Boca Raton, 1994), which is incorporated by reference herein. In IMS, gas-phase ion mobilities are determined using a drift tube with a constant electric field. Ions are separated in the drift tube on the basis of differences in their drift velocities. At low electric field strength, for example 200 V/cm, the drift velocity of an ion is proportional to the applied electric field strength, and the mobility, K, which is determined from experimentation, is independent of the applied electric field. Additionally, in IMS the ions travel through a bath gas that is at sufficiently high pressure that the ions rapidly reach constant velocity when driven by the force of an electric field that is constant both in time and location. This is to be clearly distinguished from those techniques, most of which are related to mass spectrometry, in which the gas pressure is sufficiently low that, if under the influence of a constant electric field, the ions continue to accelerate.
E. A. Mason and E. W. McDaniel in their book entitled “Transport Properties of Ions in Gases” (Wiley, N.Y., 1988), which is incorporated by reference herein, teach that at high electric field strength, for instance fields stronger than approximately 5,000 V/cm, the ion drift velocity is no longer directly proportional to the applied electric field, and K is better represented by KH, a non-constant high field mobility term. The dependence of KH on the applied electric field has been the basis for the development of high field asymmetric waveform ion mobility spectrometry (FAIMS). Ions are separated in FAIMS on the basis of a difference in the mobility of an ion at high field strength, KH, relative to the mobility of the ion at low field strength, K. In other words, the ions are separated due to the compound dependent behavior of KH as a function of the applied electric field strength.
In general, a device for separating ions according to the FAIMS principle has an analyzer region that is defined by a space between first and second spaced-apart electrodes. The first electrode is maintained at a selected dc voltage, often at ground potential, while the second electrode has an asymmetric waveform V(t) applied to it. The asymmetric waveform V(t) is composed of a repeating pattern including a high voltage component, VH, lasting for a short period of time tH and a lower voltage component, VL, of opposite polarity, lasting a longer period of time tL. The waveform is synthesized such that the integrated voltage-time product, and thus the field-time product, applied to the second electrode during each complete cycle of the waveform is zero, for instance VH tH +VL tL=0; for example +2000 V for 10 μs followed by −1000 V for 20 μs. The peak voltage during the shorter, high voltage portion of the waveform is called the “dispersion voltage” or DV, which is identically referred to as the applied asymmetric waveform voltage.
Generally, the ions that are to be separated are entrained in a stream of gas flowing through the FAIMS analyzer region, for example between a pair of horizontally oriented, spaced-apart electrodes. Accordingly, the net motion of an ion within the analyzer region is the sum of a horizontal x-axis component due to the stream of gas and a transverse y-axis component due to the applied electric field. During the high voltage portion of the waveform, an ion moves with a y-axis velocity component given by vH=KHEH, where EH is the applied field, and KH is the high field ion mobility under operating electric field, pressure and temperature conditions. The distance traveled by the ion during the high voltage portion of the waveform is given by dH=vHtH=KHEHtH, where tH is the time period of the applied high voltage. During the longer duration, opposite polarity, low voltage portion of the asymmetric waveform, the y-axis velocity component of the ion is vL=KEL, where K is the low field ion mobility under operating pressure and temperature conditions. The distance traveled is dL=vLtL=KELtL. Since the asymmetric waveform ensures that (VHtH)+(VLtL)+0, the field-time products EHtH and ELtL are equal in magnitude. Thus, if KH and K are identical, dH and dL are equal, and the ion is returned to its original position along the y-axis during the negative cycle of the waveform. If at EH the mobility KH<K, the ion experiences a net displacement from its original position relative to the y-axis. For example, if a positive ion travels farther during the positive portion of the waveform, for instance dH<dL, then the ion migrates away from the second electrode and eventually will be neutralized at the first electrode.
In order to reverse the transverse drift of the positive ion in the above example, a constant negative dc voltage is applied to the second electrode. The difference between the dc voltage that is applied to the first electrode and the dc voltage that is applied to the second electrode is called the “compensation voltage” (CV). The CV prevents the ion from migrating toward either the second or the first electrode. If ions derived from two compounds respond differently to the applied high strength electric fields, the ratio of KH to K may be different for each compound. Consequently, the magnitude of the CV that is necessary to prevent the drift of the ion toward either electrode is also different for each compound. Thus, when a mixture including several species of ions, each with a unique KH/K ratio, is being analyzed by FAIMS, only one species of ion is selectively transmitted to a detector for a given combination of CV and DV. In one type of FAIMS experiment, the applied CV is scanned with time, for instance the CV is slowly ramped or optionally the CV is stepped from one voltage to a next voltage, and a resulting intensity of transmitted ions is measured. In this way a CV spectrum showing the total ion current as a function of CV, is obtained.
In FAIMS, the optimum dispersion voltage waveform for obtaining the maximum possible ion detection sensitivity on a per cycle basis takes the shape of an asymmetric square wave with a zero time-averaged value. In practice this asymmetric square waveform is difficult to produce and apply to the FAIMS electrodes because of electrical power consumption considerations. For example, without a tuned circuit the power that is required to drive a capacitive load of capacitance C, at frequency f, with a peak voltage V and a 1:1 duty cycle square wave, is V2fC. Accordingly, if a square wave at 750 kHz, 4000 V peak voltage 1:1 duty cycle is applied to a 20 picofarad load, the theoretical power consumption will be 480 Watts produced by the sum of the squares of the voltage changes on the capacitive load of 40002+40002 multiplied by f*C. If, on the other hand, a waveform is applied via a tuned circuit with Q factor (Bandwidth 3 dB/Frequency) of 200, the power consumption is reduced to less than 2.5 Watts. Theoretically the power is P(cos(Φ) where Φ is the angle between the current and the voltage applied to the capacitive load, and P is 2V2fC. This power consumption approaches zero if the current and voltage are out of phase by 90 degrees, as they would be in a perfectly tuned LC circuit with ideal components. Similarly, if the waveform is asymmetrical with duty cycle of 2:1, as for example in a FAIMS application, then the theoretical power consumption is reduced to 333 Watts, produced by the sum of squares of the voltage changes on the capacitive load of 40002+20002+(20002−13332) times f*C.
Since a tuned circuit cannot provide a square wave, an approximation of a square wave is taken as the first terms of a Fourier series expansion. One approach is to use:
                              V          ⁡                      (            t            )                          =                                            2              3                        ⁢            D            ⁢                                                  ⁢                          sin              ⁡                              (                                  ω                  ⁢                                                                          ⁢                  t                                )                                              +                                    1              3                        ⁢            D            ⁢                                                  ⁢                          sin              ⁡                              (                                                      2                    ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    t                                    -                                      π                    /                    2                                                  )                                                                        (        1        )            Where V(t) is the asymmetric waveform voltage as a function of time, D is the peak voltage (defined as dispersion voltage DV), ω is the waveform frequency in radians/sec. The first term is a sinusoidal wave at frequency ω, and the second term is a sinusoidal wave at double the frequency of the first sinusoidal wave, 2ω. The second term is optionally represented as a cosine, without the phase shift of π/2.
In practice, both the optimization of the LC tuning and maintenance of the exact amplitude of the first and second applied sinusoidal waves and the phase angle between the two waves is required to achieve long term, stable operation of a FAIMS system powered by such an asymmetric waveform generator. Accordingly, feedback control is required to ensure that the output signal is stable and that the correct waveform shape is maintained.
In U.S. Pat. No. 5,801,379, issued on Sep. 1, 1998, which is incorporated by reference herein, Kouznetsov teaches a high voltage waveform generator having separate phase correction and amplitude correction circuits. This system uses additional components in the separate phase correction and amplitude correction circuits, thereby increasing complexity and increasing the cost of manufacturing and testing the devices. Furthermore, this system cannot be implemented in the control software, making it difficult to vary certain parameters.
It is an object of the instant invention to provide a method of optimizing asymmetric waveform generator LC tuning electronics that overcomes the limitations of the prior art.